“I’m taking every match as it comes, but I’m playing as hard as I can, the best I can do and I love it out here,” stated the 37-year-old, having earned a fascinating last-16 duel with either sister Venus or world No.1 Simona Halep.
“Either way it will be a really intense match. I'm looking forward to it.
“I honestly would love to face the world No.1. At the same time I would love for Venus to win. I haven't played the world No.1 since I've been back, I don't think. It will be good, I'll be ready for either opponent.”
Yastremska, who wasn’t even born when Serena lifted her first major back at the 1999 US Open, showed signs of nerves with an opening double fault, before Williams swatted away a forehand return winner without breaking stride to ignite an immediate break.
From there, Serena flicked a sumptuous forehand passing shot down the line to quickly post a 3-0 advantage.
Yastremska, ranked No.57, began to find her radar with a couple of heavy strikes earning a first game, and the Ukrainian had a spring in her step to the sit-down, where she read a sheet of notes.